Suman sold an article for 882 after allowing 16% discount on its marked price. Had she not allowed any discount, she would have gained 20% on the cost price. What is the cost price of the article

Options

A. 725
B. 750
C. 850
D. 875

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Understand the Given Information
- Selling Price (SP) after discount = 882
- Discount allowed = 16%
- Profit if no discount is allowed = 20%

### Step 2: Calculate the Marked Price (MP)
The formula to calculate the marked price when the selling price and discount percentage are known is:

\[ MP = \frac{SP}{(1 - \frac{Discount\%}{100})} \]

Substituting the values:

\[ MP = \frac{882}{(1 - 0.16)} = \frac{882}{0.84} \]

Calculating this gives:

\[ MP = 1050 \]

### Step 3: Relate Cost Price (CP) to Marked Price (MP)
The relationship between cost price, marked price, discount percentage, and profit percentage can be expressed as:

\[ \frac{CP}{MP} = \frac{100 - Discount\%}{100 + Profit\%} \]

Substituting the known values:

\[ \frac{CP}{1050} = \frac{100 - 16}{100 + 20} \]

This simplifies to:

\[ \frac{CP}{1050} = \frac{84}{120} \]

### Step 4: Solve for Cost Price (CP)
Cross-multiplying gives:

\[ CP \cdot 120 = 1050 \cdot 84 \]

Calculating the right side:

\[ CP \cdot 120 = 88200 \]

Now, divide both sides by 120 to find CP:

\[ CP = \frac{88200}{120} \]

Calculating this gives:

\[ CP = 735 \]

### Step 5: Final Calculation
Now we can calculate the cost price:

\[ CP = 735 \]

### Conclusion
The cost price of the article is **735**.

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